Tales from three countries: reflections during COVID-19 for mathematical education in the future

How can school mathematics prepare citizens for a democratic society? Answers to this question are not static; they change as society and its problems change. The SARS-CoV-2 pandemic with its corresponding disease COVID-19 presents such a problem: what is needed to navigate this complex situation that involves, among other things, mathematics? Using the essay genre, we use three narratives from three countries—Italy, the USA (California), and Germany—to reflect on the goals of teaching mathematics during this crisis and examine aspects of each country’s standards for mathematics education. These three stories are framed by the authors’ backgrounds, experiences, interests, their country’s situation, and response to the pandemic. We first present the three narratives and then examine common issues across them that might provide insights beyond this current crisis, for preparing students to become active citizens. In particular, we focus on three issues: (1) developing a positive mindset toward mathematics to engage with and reflect on real-world problems, (2) improving interdisciplinary connections to the sciences to better understand how science professional practices and insights are similar or different from everyday practices, and (3) considering interpersonal and collective matters beyond the individual

Designing and enacting instruction that enhances language for mathematics learning

After four decades of research and development on language in mathematics classrooms, there is consensus that enhancing language is crucial for promoting students’ mathematics learning. After briefly sketching the theoretical contexts for work on this topic, in this paper we present six design principles for instruction that enhances language for mathematics learning. We then review the research that provides an empirical foundation for these principles, (a) concerning the design of learning environments to enhance language for mathematics learning and (b) on teaching practices (including teacher moves and classroom norms) involved in the enactment of those designed learning environments. Without claiming completeness, this review of the state of development and research shows that some aspects of design and instruction that enhance language for mathematics learning have been well researched, whereas research gaps for other aspects persist

Equitable Practices in Mathematics Classrooms: Research-Based Recommendations

This paper is based on the Iris M. Carl Equity Address the author delivered at the 2012 annual meeting of the National Council of Teachers of Mathematics. That invited keynote considered the question of equitable teaching practices in mathematics classrooms for students from non-dominant communities. Although research cannot provide quick answers to this question nor can it provide a recipe for equitable teaching practices, there are research-based recommendations that can guide researchers, teachers, and administrators in developing their own approaches to supporting equitable practices in mathematics classrooms. Several resources are provided for considering this question: a definition of equity, a definition of equitable practices, a framework for organizing research findings relevant to equitable practices, and questions to consider when designing equitable mathematics instruction. This discussion is informed by a sociocultural and situated perspective on mathematical thinking, on language, and on bilingual learners (for details of that framework, see Moschkovich, 2002, 2010)

Academic literacy in mathematics for English Learners

© 2015 Elsevier Inc. This paper uses a sociocultural conceptual framework to provide an integrated view of academic literacy in mathematics for English Learners. The proposed definition of academic literacy in mathematics includes three integrated components: mathematical proficiency, mathematical practices, and mathematical discourse. The paper uses an analysis of a classroom discussion to illustrate how the three components of academic literacy in mathematics are intertwined, how academic literacy in mathematics is situated, and how participants engaged in academic literacy in mathematics use hybrid resources. The paper closes by describing the implications of this integrated view of academic literacy in mathematics for mathematics instruction for English Learners, arguing that it is important that the three components not be separated when designing instruction in general, and it is essential that mathematics instruction for English Learners address these three components simultaneously

Designing and enacting instruction that enhances language for mathematics learning - a review of the state of development and research

After four decades of research and development on language in mathematics classrooms, there is consensus that enhancing language is crucial for promoting students’ mathematics learning. After briefly sketching the theoretical contexts for work on this topic, the article presents six design principles for instruction that enhance language for mathematics learning. It then reviews the research that provides an empirical foundation for these principles, (a) concerning the design of learning environments to enhance language for mathematics learning and (b) on teaching practices (including teacher moves and classroom norms) involved in the enactment of those designed learning environments. Without claiming completeness, this review of the state of development and research shows that some aspects of design and instruction that enhance language for mathematics learning have been well researched, whereas research gaps for other aspects persist